Burst pressure in a filament/wire wound cylinder

[Kilash]

Attempting to determine an estimated burst pressure for a barrel that is made from an inner cylinder sleeve reinforced with thin fibre filament or wire winded and wrapped uniformly over the cylinder sleeve. This method of construction is used for composite oxygen/gas tanks and other high-pressure vessels. I'm attempting to apply the concept into making a barrel.

Right now, I'm assuming I can utilize the filament's tensile breaking strength and dimensions to find an overall tensile strength of the material in pounds per square inch (psi), than applying this number into Barlow's formula for thin-walled cylinder vessels. Ignoring the hoop strength of the inner sleeve for now.

So given a fibre filament with a round cross-section, and a diameter of 0.018" and a breaking strength of 50 pounds:

filament area = 0.018^2 x pi <-- assuming rectangular/square cross-section due to space usage of wound filaments.
=~ 0.000324 sq.in

Number of strands that fits in 1 sq.in of cross-section = 1/0.000324 =~ 3086 strands

Hence, axial tensile strength in psi = 3086 strands x 50 pounds =~ 154,320 psi

Apply to Barlow's formula, 0.08" wall-thickness and 1" outer-diameter cylinder:

(154,320 psi x 0.08" x 2) / 1 = 24,691.2 psi (bursting pressure)

This value seems abnormally high, I can't help feel I'm missing something in my considerations. Can someone shed some light on this?

[Gippeto]

An interesting problem ...not sure I can help but willing to have a go at it.

With a diameter of .018", the area of each strand is .000254 in2. At 50 lbs breaking strength, the material tensile strength works out to 196,850psi.

Curious as to how you derived a wall thickness of .080"?

Planning to run all the filaments around the circumference? How are you handling longitudinal stress in the barrel? Will be a pressure (stress) wave moving the length of the barrel along with the projectile.

Wrapped pressure vessels have filaments running in more than one direction.

[mrfoo]

Planning to run all the filaments around the circumference? How are you handling longitudinal stress in the barrel? Will be a pressure (stress) wave moving the length of the barrel along with the projectile.

I'd suggest a layer of unidirectional carbon fibre tow (or similar) running longitudinally, then a pair of 30° crossing wraps, effectively making a non-woven triaxial layer.

Wrapped pressure vessels have filaments running in more than one direction.

True. That said, they have a more or less constant loading, and in all directions at all locations - the loading on a barrel is neither static nor constant.

Interesting question indeed.

[Kilash]

An interesting problem ...not sure I can help but willing to have a go at it.

With a diameter of .018", the area of each strand is .000254 in2. At 50 lbs breaking strength, the material tensile strength works out to 196,850psi.

Curious as to how you derived a wall thickness of .080"?

Planning to run all the filaments around the circumference? How are you handling longitudinal stress in the barrel? Will be a pressure (stress) wave moving the length of the barrel along with the projectile.

Wrapped pressure vessels have filaments running in more than one direction.

I'm going more along the route of steel wire wound guns, as built during the 1880s to 1940s, with a single continuous length of wire simply wrapping back and forth over itself. With the pressures I'm designing for, the inner sleeve material should be able to handle the longitudinal forces (which optimistically should be simply the friction of the ammunition on the barrel walls, since I'm using a separate breech). I would probably need to built in a oversize ring or baffle at each end of the barrel to prevent the filaments from sliding or shifting longitudinally with a moving pressure wave as you said.

I'm reluctant to use the real circular area of the round filament, namely since it gives a higher tensile strength value and I want to err on the side of safety. Also I think with the way the round filament wounds over means I'm dealing with "porosity" within the mass of the walls, so the tensile strength would be less than that of solid mass of material. If I'm using a flat material, like cable lacing cord, then that would be optimal.

0.08" was just a number I pulled out from my a**, but the breaking strength and diameter of the cord is that of real life Dacron B-50 cordage used for bowstrings. These numbers just seem to high to me, it seems that if we want to, we can make a small arms barrel that would handle extremely high pressures in the tens of thousands of psi with just a tenths of an inch of barrel wall thickness made from bowstring or wire? I found something about fibreglass-wrapped shotgun, but all in all it just sounds too good to be true.

Also, in regards to wall thickness, is there a practical limit to the useful thickness in filament-wound design? I know in a solid-homogeneous design like a steel gun barrel, the practical limit for wall thickness is 1.5 times the caliber, beyond that point the extra material on the outside isn't supporting the stresses of the inner walls, and you would start getting interior fractures or deformation with over the limit pressures. Is it more or less for a filament wound design?

[Gippeto]

I'm going more along the route of steel wire wound guns, as built during the 1880s to 1940s, with a single continuous length of wire simply wrapping back and forth over itself.

Why? Lot's of work...what is it you're hoping to achieve that cannot be more readily achieved by conventional means? Damascus barrels fell out of favor for more reasons than labor intensive...simply not as strong as a steel tube.

With the pressures I'm designing for, Which are?? the inner sleeve material should be able to handle the longitudinal forces (which optimistically should be simply the friction of the ammunition on the barrel walls, since I'm using a separate breech).

Nope. Barrel will be handling stress as if it were a reservoir...will be handling a force fore and aft based on pressure and area of the bore.

I'm reluctant to use the real circular area of the round filament, namely since it gives a higher tensile strength value and I want to err on the side of safety.

That's what a safety factor is for...but build it in, don't fudge it in. My pcp builds use a 3x sf at yield.

Also I think with the way the round filament wounds over means I'm dealing with "porosity" within the mass of the walls, so the tensile strength would be less than that of solid mass of material. If I'm using a flat material, like cable lacing cord, then that would be optimal.

Porosity is one good reason why this is going to be hard to calculate.

0.08" was just a number I pulled out from my a**, but the breaking strength and diameter of the cord is that of real life Dacron B-50 cordage used for bowstrings. These numbers just seem to high to me, it seems that if we want to, we can make a small arms barrel that would handle extremely high pressures in the tens of thousands of psi with just a tenths of an inch of barrel wall thickness made from bowstring or wire? I found something about fibreglass-wrapped shotgun, but all in all it just sounds too good to be true.

More variables come into play with a rifle barrel..stiffness is a big one. Increasing stiffness can alter harmonics and improve accuracy. One of the latest crazes in high power airguns is sleeving with carbon fiber...another is tensioning the barrel using nuts or belleville springs. It's not ALL about handling pressure.

Also, in regards to wall thickness, is there a practical limit to the useful thickness in filament-wound design?

I don't know.

I know in a solid-homogeneous design like a steel gun barrel, the practical limit for wall thickness is 1.5 times the caliber,

I think weight is the deciding factor...have seen some pretty heavy barrels on bench only rifles. 1" seems to be the practical limit for carry rifles...and it's a considerable piece of steel to lug around.

beyond that point the extra material on the outside isn't supporting the stresses of the inner walls, and you would start getting interior fractures or deformation with over the limit pressures.

Over the limit pressures? Why over...with an appropriate safety factor, the fail point should NEVER be reached.

Is it more or less for a filament wound design?

Don't know. Have read that in "sleeved" design, the theoretical burst pressure is usually under-rated...as each layer begins to reach yield, it transfers an increasing percentage of its load to the next layer...and so on. In theory, two steel tubes sleeved together would have a higher pressure rating than a single steel tube of the same total wall thickness.

[Kilash]

Why? Lot's of work...what is it you're hoping to achieve that cannot be more readily achieved by conventional means? Damascus barrels fell out of favor for more reasons than labor intensive...simply not as strong as a steel tube.

Simply to see if I can. I can easily order a piece of seamless 4130 tubing that would be more than what I need for about $15, but then I won't be asking this question in the first place. Mind you, I'm not here to achieve performance equal or better than metal construction, composite over-wraps have the huge disadvantage of more creep and elongation when stressed than an equivalent monobloc design (10% at max load for Dacron), hell that alone would throw accuracy and projectile obturation out the door. No, this completely an academic experiment, I just want to see if non-metal methods of barrel constructions are possible for high pressures.

With the pressures I'm designing for, Which are?? the inner sleeve material should be able to handle the longitudinal forces (which optimistically should be simply the friction of the ammunition on the barrel walls, since I'm using a separate breech).

Somewhere between 2000 - 4000 psi peak. I'm guessing that pressure wave you talked about would introduce longitudinal forces to the barrel? My inner sleeve should handle it, it can't be more than a few hundred pounds of force.

That's what a safety factor is for...but build it in, don't fudge it in. My pcp builds use a 3x sf at yield.

I have plans to test my prototype to failure, but yes I would be using a SF of at least 2 times. But to find the SF, I need to figure out the correct basis for the design in the first place XD.

Porosity is one good reason why this is going to be hard to calculate.

So I been looking around and I found an Indian publication on composite overwrap PV construction, looks like they're using a modified Lame's equation (with a tangential component, I guess to account for the helical direction of their filament wounding) where the ultimate tensile strength of the filament material is directly inputted. So I guess I'm on the right track here with Barlow's, still I would assume the circular round filaments of B-50 to be square.

Just some insight, The British and Japanese used rectangular/ribbon drawn steel wire for their battleship guns, so they didn't have my same issue with "porosity". The British 15-in/42 Mark I used about 170 miles (274 km) of wire to reinforce an inner steel tube. The wire was rated at tensile strengths over 220,000 psi.

Over the limit pressures? Why over...with an appropriate safety factor, the fail point should NEVER be reached.

You'll be surprise with what past military engineers have attempted. In any case, I was just illustrating that there IS a practical limit to how thick you can make a barrel. A lot of people just assume because you have a ton of wall, your barrel would be safe for whatever pressures. NOT TRUE! In a homogeneous monobloc barrel, the highest pressure you can theoretically handle is equivalent to the tensile strength of the material used. This is absent of any sort of autofrettaging or pre-stressing technique. If you use a material with a tensile strength of 5,000 psi, no matter how thick you make a barrel out of it, it would never handle more than 5,000 psi of pressure, whether hydraulic or gas. The practical limits are WAY below that of course.

Don't know. Have read that in "sleeved" design, the theoretical burst pressure is usually under-rated...as each layer begins to reach yield, it transfers an increasing percentage of its load to the next layer...and so on. In theory, two steel tubes sleeved together would have a higher pressure rating than a single steel tube of the same total wall thickness.

That is if the out layers are pre-stressed over the inner ones, as in a built-up gun. But this raises a good point, a filament wound design is equivalent to many thin sleeves encompassing one another. More justification that my method is close to being correct?

[Gippeto]

Thinking you need the help of someone a good deal more educated on the subject than I. Suggest you contact D.Hall.

As far as length wise stresses....going with .080" wall and 1" od...gives a bore of .84"...@ 4000psi, you're looking at a force of 2215 lbs. Won't take much of a tube to handle it in tension, but it's still a considerable amount of force. With pcp airguns, have seen one fellow blow the barrel clear of the receiver by underestimating the forces involved.

[Kilash]

Thinking you need the help of someone a good deal more educated on the subject than I. Suggest you contact D.Hall.

As far as length wise stresses....going with .080" wall and 1" od...gives a bore of .84"...@ 4000psi, you're looking at a force of 2215 lbs. Won't take much of a tube to handle it in tension, but it's still a considerable amount of force. With pcp airguns, have seen one fellow blow the barrel clear of the receiver by underestimating the forces involved.

Thanks for your input on this Gippeto, appreciate it . I think the only sure way to find out is build the prototype and a nice sturdy testing bunker. BTW, my prototype design is going to be a 0.38" bore, as you said its a lot of work, so the less thread I have to wind, the better XD.

[mrfoo]

Looking at the patents might be of use; it certainly seems that the idea should work.

For example, http://www.google.com/patents/US4685236 "Graphite/metal matrix gun barrel", and the various referenced patents.

I've not found anything with a *single* layer of helically wound reinforcement, though.